Question

How long after closing the switch will the energy stored in the inductor reach one-half of its maximum value?

Answer 1

$\left(\frac{1}{2}L{i}^2\right)=\left(\frac{1}{2}L{i_0}^2\right)/2$
$\therefore i=\frac{i_0}{\sqrt{2}}$
Now apply
$i=i_0(1-e^{-t/{\tau }_L})$
where
${\tau }_L=\frac{L}{R}$